Problem: Which decimal is equivalent to $\dfrac{13}{11}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $1.\overline{1}$ (Choice B) B $1.\overline{181}$ (Choice C) C $1.\overline{18}$ (Choice D) D $1.1\overline{8}$
Answer: $ \dfrac{13}{11}$ represents $13 \div 11$. ${1}$ ${1}$ ${1}$ ${3}$ ${0}$ $\text{How many times does }11\text{ go into }{13}\text{?}$ ${1}$ ${1}$ ${1}$ $-$ ${2}$ ${13}\div11={1}\text{ with a remainder of }{2}$ ${0}$ ${.}$ ${.}$ $\text{Write in a decimal and a zero.}$ $\text{How many times does }11\text{ go into }{20}\text{?}$ ${0}$ ${0}$ ${1}$ ${1}$ ${1}$ $-$ ${9}$ ${20}\div11={1}\text{ with a remainder of }{9}$ $\text{How many times does }11\text{ go into }{90}\text{?}$ ${0}$ ${0}$ ${8}$ ${8}$ ${8}$ $-$ ${2}$ ${90}\div11={8}\text{ with a remainder of }{2}$ $\text{How many times does }11\text{ go into }{20}\text{?}$ ${0}$ ${0}$ ${1}$ ${1}$ ${1}$ $-$ ${9}$ ${20}\div11={1}\text{ with a remainder of }{9}$ $\text{How many times does }11\text{ go into }{90}\text{?}$ ${0}$ ${0}$ ${8}$ ${8}$ ${8}$ ${8}$ $-$ ${2}$ ${2}$ ${90}\div11={8}\text{ with a remainder of }{2}$ Notice how the decimal is repeating and will continue to repeat as we bring down more zeros. So $\dfrac{13}{11}$ is equivalent to $1.\overline{18}$.